SLI (Supplemental Liability Insurance), or third party liability is not offered by AMEX nor any other credit card I can think of.

SLI is insurance that covers you for injuring another car/driver or property damage to the other car if you are involved in an accident. It is usually cheaper than CDW/LDW.

Most people dont elect to buy it because their personal insurance covers them for damage that they inflict on other people's cars while renting a car.

However if you don't have a personal insurance policy then you do not have this level of protection. Although some states mandate that some level of 3rd party damage insurance be included with a rental contract but it is minimal coverage $10,000-100,000 coverage, depending on state.

If you are involved in a huge accident where you are at fault and it involves an expensive car, and/or bodily damage to the other driver/passengers, you are liable for all damages over the minimal coverage, dependent on the state you rent from.

Purchasing SLI will increase your coverage significantly.